Determinant of 10x10 Matrix

I am trying to figure out the formula for the determinant of a 10x10 matrix. I was told to use row reducation method, but I am not really sure what it is. I never took Linear Algebra. Can someone please help me.

It's going to be quite tedious even if you were to row-reduce it before finding its determinant. Some special matrices have easy determinants, so maybe you could see if the matrix for which you are trying to evaluate the determinant has some property which allows you to compute its determinant easily.

EDIT: I see that you say you are trying to "figure out the formula". There's a recursive method for finding the determinants of an arbitrary nxn matrix. It's known as cofactor expansion.

Umm I can't go numerical... I need to do it in terms of formulas.... And no, diagonals arent allowed. What can I do? Can someone help me determine the forumla? please

Is this question from a textbook? If so, then perhaps it's best if you were to post the exact problem. The problem with devising a formula for the determinant of a 10x10 matrix is that it would require far too many variables, at least 100 variables would be needed, each for every entry of the matrix. I doubt any textbook problem would require such to be done.

Is this question from a textbook? If so, then perhaps it's best if you were to post the exact problem. The problem with devising a formula for the determinant of a 10x10 matrix is that it would require far too many variables, at least 100 variables would be needed, each for every entry of the matrix. I doubt any textbook problem would require such to be done.

Not in a textbook. My proffesor for Diffiq said if anyone figures out the forumal for the dertminant of a 10x10, they automatically get an A in the class.

Finding the formula is really simple. You'd just need several pages to write/print it, and there would be 100 variables. So you'd be very likely to make a mistake somewhere if you tried to do it by hand.

I doubt that your professor would actually give an A for it though since it is extremely easy.

Hell, I wonder if this would suffice: (Let [tex]a_{i,j}[/tex] denote the i,jth entry of the matrix)
[tex]\sum_{\sigma \in S_{10}} \text{sgn}(\sigma) \sum_{i=1}^{10} a_{i, \sigma(i)}[/tex]
because that is one way to write the formula. It's called Leibniz's formula for the determinant. Of course you'd need to know what [tex]S_{10}[/tex] is and what the sign of an element of [tex]S_{10}[/tex] means as well as how to interpret the summation signs